10.4122/1.1000000520
Van Esch, John
John
Van Esch
j.m.vanesch@geodelft.nl
Van Esch, John
John
Van Esch
j.m.vanesch@geodelft.nl
Adaptive Multi Scale modeling of groundwater flow and transport
XVI International Conference on Computational Methods in Water Resources
2006
2006
Usually the permeability tensor is the most dominant parameter affecting groundwater
flow and transport, while it is also the most heterogeneous parameter. Permeability
can be measured on laboratory scale and subsequently a spatially correlated random
field generator is often used to construct a field scale model. This procedure
results in a very fine grid with discrete tensor coefficients for each cell. To
reduce the number of unknowns in the flow model fine scale permeabilities have to be
upscaled to coarse scale permeabilities that relate the spatial averaged pressure,
flux and dissipation to each other. However exact values cannot be found in general
and traditional upscaling methods depend heavily on the local boundary conditions
chosen.
This paper presents an operator based scaling technique that is applied for
communication between scales in combination with adaptive mesh refinement that
balances the loss in accuracy due to the averaging procedure. The technique is used
to solve three dimensional groundwater flow and transport problems in partly
saturated highly heterogeneous porous media. The subdomain collocation finite
element method discretizes the flow and transport equation. Both sets of linearized
equations are then solved sequentially in a number of multigrid cycles where mesh
refinement is restricted to elements for which a local error criterion does not
hold. Picard iterations resolve the non-linearities due to unsaturated flow and
density and viscosity coupling.
One example illustrates this adaptive multi scale technique by simulating flow and
transport through a heterogeneous embankment. The application shows the reduction of
computational work required to obtain the desired level of accuracy by refining the
mesh only in regions of interest where high concentration fronts or high
permeability contrast exist.